Phases and Phase transitions of U(1)$\times$SU(2) symmetric holographic matter

TL;DR

This paper explores the phase diagram and symmetry breaking patterns of a holographic model with U(1)$\times$SU(2) symmetry, revealing second order and first order phase transitions through analytical and numerical methods.

Contribution

It provides a comprehensive analysis of symmetry breaking and phase transitions in a holographic U(1)$\times$SU(2) model using Einstein-Yang-Mills theory, including IR asymptotics and phase diagrams.

Findings

Identified all possible symmetry breaking patterns with chemical potentials.

Derived IR asymptotics analytically for 2+1 and 3+1 dimensions.

Mapped the full phase diagram showing second and first order transitions.

Abstract

The phase diagram and symmetry breaking patterns of a holographic CFT with U(1)$\times$SU(2) symmetry are analyzed using the simplest holographic action, namely Einstein-Yang-Mills (YM) theory with a negative cosmological constant. This is relevant for both condensed matter and QCD applications. With a U(1) and an "isospin" chemical potential turned on, we determine all possible symmetry breaking patterns, which are associated to the condensation of spin-one order parameters. The possible IR asymptotics of the Einstein-YM solutions are derived analytically, both for 2+1 and 3+1 boundary dimensions. The competing solutions are then computed numerically, both at zero and non-zero temperature, from which the full three-dimensional phase diagram is determined. We find a surface of second order phase transitions that separate uncondensed and condensed phases. In some regions with a large fraction of charged to neutral degrees of freedom, the phase transition becomes first order.